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Triangle Congruence: SSS and HL Answers

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Examine this figure. Which two pieces of information, if true, would help to prove that ΔLMP ≅ ΔNMP by HL? Select two options.

A
Point P is the midpoint of MK.
B
Line MK is the perpendicular bisector of LN.
C
ML ≅ MP
D
ML ≅ MN
E
PK ≅ PK
2
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Which shows two triangles that are congruent by the SSS congruence theorem?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

The triangles are congruent by SSS and HL.

Question illustration
r
reflection only
t
translation only
r
reflection, then translation
r
rotation, then translation
4

The triangles are congruent by SSS or HL.

Question illustration
t
translation only
r
reflection only
r
rotation, then reflection
r
rotation, then translation
5

Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.

Question illustration
T
They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
T
They are congruent because opposite sides of a parallelogram are congruent.
T
They are not congruent because only one pair of corresponding sides is congruent.
T
They are not congruent because only two pairs of corresponding sides are congruent.
6

Triangles S U V and R U W are connected at point U. Angles S U V and W U T are right angles. The length of hypotenuse S V is 2 x + 9 and the length of hypotenuse W T is 4 x minus 1. Sides V U and U W are congruent.

Question illustration
A
2
B
3
C
4
D
5
7

Question text not available

Question illustration
2
2
3
3
4
4
7
7
8

The triangles are congruent by the SSS congruence theorem.

Question illustration
A
rotation only
B
reflection only
C
translation, then rotation
D
translation, then reflection
9

The triangles shown are congruent by the SSS congruence theorem.

Question illustration
A
rotation, then reflection, then translation
B
rotation, then translation, then reflection
C
translation, then reflection, then rotation
D
translation, then rotation, then reflection
10

The triangles are congruent by the SSS congruence theorem.

Question illustration
r
reflection, then dilation
r
reflection, then translation
r
rotation, then translation
r
rotation, then reflection
11

The triangles shown are congruent by the SSS congruence theorem.

Question illustration
A
rotation, then reflection, then translation
B
rotation, then translation, then reflection
C
translation, then reflection, then rotation
D
translation, then rotation, then reflection
12

Question text not available

Question illustration
A
2
B
3
C
4
D
7
13

Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.

Question illustration
A
They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
B
They are congruent because opposite sides of a parallelogram are congruent.
C
They are not congruent because only one pair of corresponding sides is congruent.
D
They are not congruent because only two pairs of corresponding sides are congruent.
14

The triangles are congruent by the SSS congruence theorem.

Question illustration
A
rotation only
B
reflection only
C
translation, then rotation
D
translation, then reflection
15

Point H is the midpoint of side FK.

Question illustration
A
1
B
3
C
6
D
8
16

Which shows two triangles that are congruent by the SSS congruence theorem?

A
Triangles A B C and D E C are connected at point C. Angles A B C and C E D are right angles. The lengths of sides A B and E D are congruent.
Option A
B
Triangles A B C and D E C are connected at point C. The lengths of sides A B and D E are congruent. The lengths of sides B C and C D are congruent.
Option B
C
Triangles A B C and D E C are connected at point C. The lengths of sides A C and C E are congruent. Angles B A C and C E D are congruent.
Option C
D
Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent. The lengths of B C and D C are congruent.
Option D
17

Triangle ABC is congruent to A'BC' by the HL theorem.

Question illustration
A
dilation
B
reflection
C
rotation
D
translation
18

The triangles are congruent by the SSS congruence theorem.

Question illustration
A
reflection, then rotation
B
reflection, then translation
C
rotation, then translation
D
rotation, then dilation
19

The triangles are congruent by SSS or HL.

Question illustration
A
translation only
B
reflection only
C
rotation, then reflection
D
rotation, then translation
20

Examine this figure. Which two pieces of information, if true, would help to prove that ΔLMP ≅ ΔNMP by HL? Select two options.

A
Point P is the midpoint of MK.
B
Line MK is the perpendicular bisector of LN.
C
ML ≅ MP
D
ML ≅ MN
E
PK ≅ PK

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